Curves and Isometries

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Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Explores isometries, reflections, rotations, and translations in space, as well as the structure theorem and configurations of planes and lines.

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Covers the preservation of isometry by rotations and symmetries.

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

Explores the theory and applications of helical curves, focusing on circular helices with various parameters.

Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Explores the modern definition of symmetry and its practical applications.